Laitinen et al. (1983) proposed an extension to the Working's (1943) Model which allows the marginal share to be a linear function of the corresponding budget share. In this paper, we derive the conditional (within a group of goods) version of Laitinen's Generalized Working's Model which is an important and useful generalization of the popular Working's Model with respect to the conditional case. We then use the new model to analyse the Australian energy consumption patterns conditionally for electricity, gas, petrol, and diesel using the most recent ABS Household Expenditure Survey 2015–2016 data. We found some interesting energy consumption patterns in Australia at (a) states/territories (b) remoteness of location and (c) income group levels. The results indicate that energy, as a group, is a necessity for all Australian households irrespective of their income and where they live. Within specified energy group, electricity is a necessity and petrol and diesel are luxuries for households across Australia and households of all income groups. Gas switches between being a necessity or a luxury based on the state/territory and level of remoteness. This is an appealing result that illustrates the valuable property of the Generalized Working's Model whereby a good can switch from a luxury to a necessity and vice versa, something that is ruled out in the original Working's Model.